{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "416241e2-847b-4136-a4f8-9a0c390881f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import torch.nn as nn\n",
    "from torch.utils.data import DataLoader, TensorDataset\n",
    "from torch.utils.data import random_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "e3fe0253-887d-43ea-a1a3-bd9d9899f311",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x, y):\n",
    "    return x ** 2 + 2 * y ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "85fc8a90-0900-4ff6-9aaa-2be09717c262",
   "metadata": {},
   "outputs": [],
   "source": [
    "num_samples = 1000\n",
    "X = torch.rand(num_samples)\n",
    "Y = torch.rand(num_samples)\n",
    "Z = f(X, Y) + torch.randn(num_samples)\n",
    "\n",
    "dataset = torch.stack([X, Y, Z], dim=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b717780b-854f-4580-9aa1-9dd72dbefaed",
   "metadata": {},
   "outputs": [],
   "source": [
    "train_size = int(0.7 * len(dataset))\n",
    "test_size = len(dataset) - train_size\n",
    "\n",
    "train_dataset, test_dataset = random_split(dataset=dataset, lengths=[train_size, test_size])\n",
    "\n",
    "train_dataloader = DataLoader(TensorDataset(train_dataset.dataset.narrow(1, 0, 2), train_dataset.dataset.narrow(1, 2, 1)))\n",
    "test_dataloader = DataLoader(TensorDataset(test_dataset.dataset.narrow(1, 0, 2), test_dataset.dataset.narrow(1, 2, 1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a541c8fe-99f0-41cf-8e34-a1de50899d65",
   "metadata": {},
   "outputs": [],
   "source": [
    "class Model(nn.Module):\n",
    "    def __init__(self):\n",
    "        super().__init__()\n",
    "        self.hidden = nn.Linear(2, 8)\n",
    "        self.relu = nn.ReLU()\n",
    "        self.output = nn.Linear(8, 1)\n",
    "\n",
    "    def forward(self, x):\n",
    "        x = self.hidden(x)\n",
    "        x = self.relu(x)\n",
    "        x = self.output(x)\n",
    "        return x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "600639ca-2a31-4fd9-998e-396a929c00a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 超参数\n",
    "num_epochs = 100\n",
    "learning_rate = 0.1\n",
    "\n",
    "# 损失函数\n",
    "loss_fn = nn.MSELoss()\n",
    "\n",
    "for with_scheduler in [False, True]:\n",
    "    train_losses = []\n",
    "    test_losses = []\n",
    "\n",
    "    model = Model()\n",
    "    optimizer = torch.optim.SGD(model.parameters(), lr=learning_rate)\n",
    "\n",
    "    # 学习率调节器\n",
    "    scheduler = torch.optim.lr_scheduler.ExponentialLR(optimizer, gamma=0.99)\n",
    "\n",
    "    for epoch in range(num_epochs):\n",
    "        model.train()\n",
    "        train_loss = 0\n",
    "        for inputs, targets in train_dataloader:\n",
    "            optimizer.zero_grad()\n",
    "            outputs = model(inputs)\n",
    "            loss = loss_fn(outputs, targets)\n",
    "            loss.backward()\n",
    "            optimizer.step()\n",
    "            train_loss += loss.item()\n",
    "\n",
    "        train_loss /= len(train_dataloader)\n",
    "        train_losses.append(train_loss)\n",
    "\n",
    "        model.eval()\n",
    "        test_loss = 0\n",
    "        with torch.no_grad():\n",
    "            for inputs, targets in test_dataloader:\n",
    "                outputs = model(inputs)\n",
    "                loss = loss_fn(outputs, targets)\n",
    "                test_loss += loss.item()\n",
    "\n",
    "            test_loss /= len(test_dataloader)\n",
    "            test_losses.append(test_loss)\n",
    "\n",
    "        if with_scheduler:\n",
    "            scheduler.step()\n",
    "\n",
    "    plt.figure(figsize=(8, 4))\n",
    "    plt.plot(range(num_epochs), train_losses, label='Train')\n",
    "    plt.plot(range(num_epochs), test_losses, label='Test')\n",
    "    plt.title(\"{0} lr_scheduler\".format(\"With\" if with_scheduler else \"Without\"))\n",
    "    plt.legend()\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de868fee-909b-4aee-825e-87504b8d943d",
   "metadata": {},
   "source": [
    "### 常见的学习率衰减器\n",
    "- 学习率衰减  \n",
    "  scheduler = torch.optim.lr_scheduler.StepLR(optimizer, step_size=100, gamma=0.5)  \n",
    "- 指数衰减  \n",
    "  scheduler = torch.optim.lr_scheduler.ExponentialLR(optimizer, gamma=0.99)  \n",
    "- 余弦学习率  \n",
    "  scheduler = torch.optim.lr_scheduler.CosineAnnealingLR(optimizer, T_max=100, eta_min=0.00001)  \n",
    "- 自定义学习率  \n",
    "  scheduler = torch.optim.lr_scheduler.LambdaLR(optimizer, lr_lambda=labmda epoch: 0.99 ** epoch)  \n",
    "- 预热  \n",
    "  warmup_steps = 20  \n",
    "  scheduler = torch.optim.lr_scheduler.LambdaLR(optimizer, lr_lambda=labmda t: min(t / warmup_steps, 0.001))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.21"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
